I also was unable to use this patch, because it references "$PATH" on line 8 of init.rb, which is an undefined global.

I was able to get the driver to work using the following steps:

Extract the files contained within dorb_sqlite3.rb to the current directory by running:

ruby dorb_sqlite3.rb --tar2rubyscript-justextract
This puts the files in .\dorb_sqlite3.
# Copying .\dorb_sqlite3\files\sqlite3_c.so to your ruby msvcrt dir. Mine is C:\ruby\lib\ruby\site_ruby\1.8\i386-msvcrt\
# To test I ran the following from an irb: